Finite groups

C-group

In mathematical group theory, a C-group is a group such that the centralizer of any involution has a normal Sylow 2-subgroup. They include as special cases CIT-groups where the centralizer of any involution is a 2-group, and TI-groups where any Sylow 2-subgroups have trivial intersection. The simple C-groups were determined by , and his classification is summarized by , 16.4). The classification of C-groups was used in Thompson's classification of N-groups.The simple C-groups are * the projective special linear groups PSL2(p) for p a Fermat or Mersenne prime * the projective special linear groups PSL2(9) * the projective special linear groups PSL2(2n) for n≥2 * the projective special linear groups PSL3(q) for q a prime power * the Suzuki groups Sz(22n+1) for n≥1 * the projective unitary groups PU3(q) for q a prime power (Wikipedia).

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Related pages

Sylow 2-subgroup | N-group (finite group theory) | Group theory